材力课设.zip_actual7u3_diseaseuvv_purposeujv_材料力学 matlab_材料力学课设

%材料力学课程设计第一题所有问题的求解 %1.以下求解未知力矩 %参考数据q=15300,FB=4400; clc;clear; l1=1.1;l2=1.6;l3=3.1;l4=1.6;l5=2.1;FA=2680; q=input('输入q的值（单位N/m）：'); FB=input('输入FB的值（单位N）：'); close all; MC=-FA*l1;MG=-FB*l5; w2=q*l2^3/12;w3=q*l3^3/12;w4=q*l4^3/12; A=[2*(l2+l3),l3;l3,2*(l3+l4)]; C=[-6*(w2/2+w3/2)-MC*l2;-6*(w3/2+w4/2)-MG*l4]; RE=A\C; fprintf('\n1.求解未知力矩的结果：\n') MD=RE(1);MF=RE(2); fprintf('MD=%.1fNm , MF=%.1fNm\n\n',MD,MF); %以下求解支反力，需要调用M函数F_Liang.m display('第一段梁求解结果:'); [FC,FD1]=F_Liang(FA,0,MC,MD,l2,q); fprintf('FC=%.1fN , FD1=%.1fN\n\n',FC,FD1); display('第二段梁求解结果:'); [FD2,FF1]=F_Liang(0,0,MD,MF,l3,q); fprintf('FD2=%.1fN , FF1=%.1fN\n\n',FD2,FF1); display('第三段梁求解结果:'); [FF2,FG]=F_Liang(0,FB,MF,MG,l4,q); fprintf('FF2=%.1fN , FG=%.1fN\n\n',FF2,FG); FD=FD1+FD2;FF=FF1+FF2; display('综合得到多跨梁各支座的支反力如下：') fprintf('FC=%.0fN\nFD=%.0fN\nFF=%.0fN\nFG=%.0fN\n\n\n',FC,FD,FF,FG); %2.以下画出内力图 %求解剪力方程，画出剪力图 FQ1max=-FA;FQ1min=-FA; FQ2max=FC-FA;FQ2min=FC-FA-l2*q; FQ3max=FC-FA-l2*q+FD;FQ3min=FC-FA-l2*q+FD-l3*q; FQ4max=FC-FA-l2*q+FD-l3*q+FF;FQ4min=FC-FA-l2*q+FD-l3*q+FF-l4*q; FQ5min=FC-FA-l2*q+FD-l3*q+FF-l4*q+FG;FQ5max=FQ5min; FQ1=-FA; FQ2=subs(@(x)FQ2max-q*(x-l1)); FQ3=subs(@(x)FQ3max-q*(x-l1-l2)); FQ4=subs(@(x)FQ4max-q*(x-l1-l2-l3)); FQ5=FQ5max; disp('2.第一段到第五段梁的剪力方程（单位：N）分别为：') fprintf('FQ1=%s\n',char(vpa(FQ1,7))) fprintf('FQ2=%s\n',char(vpa(FQ2,7))) fprintf('FQ3=%s\n',char(vpa(FQ3,7))) fprintf('FQ4=%s\n',char(vpa(FQ4,7))) fprintf('FQ5=%s\n\n',char(vpa(FQ5,7))) figure(1); hold on; ezplot(num2str(FQ1),[0,l1]); ezplot(FQ2,[l1,l1+l2]); ezplot(FQ3,[l1+l2,l1+l2+l3]); ezplot(FQ4,[l1+l2+l3,l1+l2+l3+l4]); ezplot(num2str(FQ5),[l1+l2+l3+l4,l1+l2+l3+l4+l5]); xlim([0,l1+l2+l3+l4+l5]); ylim([-5e4,5e4]); plot([l1,l1],[FQ1min,FQ2max],'--'); plot([l1+l2,l1+l2],[FQ2min,FQ3max],'--'); plot([l1+l2+l3,l1+l2+l3],[FQ3min,FQ4max],'--'); plot([l1+l2+l3+l4,l1+l2+l3+l4],[FQ4min,FQ5max],'--'); plot([0,l1+l2+l3+l4+l5],[0,0],'k'); text(0.25,FQ1max-0.35e4,num2str(FQ1max)); text(l1-0.45,FQ2max+0.35e4,num2str(FQ2max)); text(l1+l2-0.45,FQ2min-0.35e4,num2str(FQ2min)); text(l1+l2-0.45,FQ3max+0.35e4,num2str(FQ3max)); text(l1+l2+l3-0.45,FQ3min-0.35e4,num2str(FQ3min)); text(l1+l2+l3-0.45,FQ4max+0.35e4,num2str(FQ4max)); text(l1+l2+l3+l4-0.45,FQ4min-0.35e4,num2str(FQ4min)); text(8,FQ5max+0.35e4,num2str(FQ5max)); xlabel('x /m');ylabel('FQ /N');title('剪力图'); %求解弯矩方程，画出弯矩图 syms x; M1=int(num2str(-FA),0,x);M1r=subs(M1,x,l1); M2=int(FQ2,l1,x)+M1r;M2r=subs(M2,x,l1+l2); M3=int(FQ3,l1+l2,x)+M2r;M3r=subs(M3,x,l1+l2+l3); M4=int(FQ4,l1+l2+l3,x)+M3r;M4r=subs(M4,x,l1+l2+l3+l4); M5=int(num2str(FQ5max),l1+l2+l3+l4,x)+M4r;M5r=subs(M5,x,l1+l2+l3+l4+l5); [x2,M2max]=fminbnd(eval(['@(x)',char(-M2)]),l1,l1+l2);M2max=-M2max; [x3,M3max]=fminbnd(eval(['@(x)',char(-M3)]),l1+l2,l1+l2+l3);M3max=-M3max; [x4,M4max]=fminbnd(eval(['@(x)',char(-M4)]),l1+l2+l3,l1+l2+l3+l4);M4max=-M4max; disp('第一段到第五段梁的弯矩方程(单位：Nm)分别为：'); fprintf('M1=%s\n',char(vpa(expand(M1),7))); fprintf('M2=%s\n',char(vpa(expand(M2),5))); fprintf('M3=%s\n',char(vpa(expand(M3),6))); fprintf('M4=%s\n',char(vpa(expand(M4),6))); fprintf('M5=%s\n\n',char(vpa(expand(M5),7))); fprintf('剪力图和弯矩图如图所示\n\n\n'); figure(2); hold on;box off; ezplot(M1,[0,l1]); ezplot(M2,[l1,l1+l2]); ezplot(M3,[l1+l2,l1+l2+l3]); ezplot(M4,[l1+l2+l3,l1+l2+l3+l4]); ezplot(M5,[l1+l2+l3+l4,l1+l2+l3+l4+l5]); plot([0,l1+l2+l3+l4+l5],[0,0],'k'); xlim([0,l1+l2+l3+l4+l5]); ylim([-1.2e4,1e4]); plot([l1,l1],[0,M1r],'--'); plot([l1+l2,l1+l2],[0,M2r],'--'); plot([l1+l2+l3,l1+l2+l3],[0,M3r],'--'); plot([l1+l2+l3+l4,l1+l2+l3+l4],[0,M4r],'--'); %text(l1-0.45,FQ2max+0.35e4,num2str(FQ2max)); %text(l1-0.45,M1r-0.6e3,num2str(M1r)); %text(x2-0.3,0.6e3,'num2str(M2max)'); %text(x2,-0.7e3,'\bf\downarrow'); %text(l1+l2-0.3,M2r-0.6e3,num2str(M2r)); %text(x3-0.3,M3max+0.6e3,num2str(M3max)); %text(l1+l2+l3-0.3,M3r-0.6e3,num2str(M3r)); %text(x4-0.3,M4max+0.6e3,num2str(M4max)); %text(l1+l2+l3+l4-0.15,M4r-0.6e3,num2str(M4r)); title('弯矩图');xlabel('x /m');ylabel('Mz /Nm'); %3.以下画出最大弯曲正应力的变化曲线 fprintf('3.最大弯曲正应力的变化曲线如图所示\n\n\n'); h1=0.1;h2=0.12;h3=0.11; b1=0.06;b2=0.08;b3=0.07; t=0.005;E=210e9; Wz=@(b,h)(b*h^3-(b-2*t)*(h-2*t)^3)/(6*h); Wz1=Wz(b1,h1); Wz2=Wz(b2,h2); Wz3=Wz(b3,h3); sigma1=abs(M1/Wz1); sigma2=abs(M2/Wz2); sigma3=abs(M3/Wz2); sigma4=abs(M4/Wz2); sigma5=abs(M5/Wz3); figure(3); hold on; ezplot(sigma1,[0,l1]); ezplot(sigma2,[l1,l1+l2]); ezplot(sigma3,[l1+l2,l1+l2+l3]); ezplot(sigma4,[l1+l2+l3,l1+l2+l3+l4]); ezplot(sigma5,[l1+l2+l3+l4,l1+l2+l3+l4+l5]); plot([0,l1+l2+l3+l4+l5],[0,0],'k'); xlim([0,l1+l2+l3+l4+l5]); ylim([0,2.5e8]); Y12=max(subs(sigma1,x,l1),subs(sigma2,x,l1)); Y23=max(subs(sigma4,x,l1+l2+l3+l4),subs(sigma5,x,l1+l2+l3+l4)); plot([l1,l1],[0,Y12],'--'); plot([l1+l2+l3+l4,l1+l2+l3+l4],[0,Y23],'--'); xlabel('x /m');ylabel('\sigma_{max} /Pa');title('最大弯曲正应力变化曲线'); %4.以下求最大挠度 %求各段挠度 syms C1 D1 C2 D2 C3 D3 C4 D4 C5 D5; v2=int(int(M2*2/(Wz2*h2*E)))+C2*x+D2; [C2,D2]=solve(subs(v2,x,l1),subs(v2,x,l1+l2)); v3=int(int(M3*2/(Wz2*h2*E)))+C3*x+D3; [C3,D3]=solve(subs(v3,x,l1+l2),subs(v3,x,l1+l2+l3)); v4=int(int(M4*2/(Wz2*h2*E)))+C4*x+D4; [C4,D4]=solve(subs(v4,x,l1+l2+l3),subs(v4,x,l1+l2+l3+l4)); theta2=subs(diff(v2,x)); theta2C=subs(theta2,x,l1); theta4=subs(diff(v4,x)); theta4G=subs(theta4,x,l1+l2+l3+l4); v1=int(int(M1*2/(Wz1*h1*E)))+C1*x+D1; theta1=subs(diff(v1,x)); theta1C=subs(theta1,x,l1); [C1,D1]=solve(theta1C-theta2C,subs(v1,x,l1)); v5=int(int(M5*2/(Wz3*h3*E)))+C5*x+D5; theta5=subs(diff(v5,x)); theta5G=subs(theta5,x,l1+l2+l3+l4); [C5,D5]=solve(theta5G-theta4G,subs(v5,x,l1+l2+l3+l4)); v1=subs(v1); v2=subs(v2); v3=subs(v3); v4=subs(v4); v5=subs(v5); %画出挠曲线 figure(4); hold on;box off; ezplot(v1,[0,l1]); ezplot(v2,[l1,l1+l2]); ezplot(v3,[l1+l2,l1+l2+l3]); ezplot(v4,[l1+l2+l3,l1+l2+l3+l4]); ezplot(v5,[l1+l2+l3+l4,l1+l2+l3+l4+l5]); plot([0,l1+l2+l3+l4+l5],[0,0],'k'); xlim([0,l1+l2+l3+l4+l5]); ylim([-0.05,0.01]); xlabel('x /m');ylabel('v /m');title('挠曲线图'); [v1x,v1min]=fminbnd(eval(['@(x)',char(v1)]),0,l1); [v2x,v2max]=fminbnd(eval(['@(x)',char(-v2)]),l1,l1+l2);v2max=-v2max; [v3x,v3min]=fminbnd(eval(['@(x)',char(v3)]),l1+l2,l1+l2+l3); [v4x,v4max]=fminbnd(eval(['@(x)',char(-v4)]),l1+l2+l3,l1+l2+l3+l4);v4max=-v4max; [v5x,v5min]=fminbnd(eval(['@(x)',char(v5)]),l1+l2+l3+l4,l1+l2+l3+l4+l5); text(0.2,v1min-0.003,num2str(v1min)); text(v2x,v2max+0.003,num2str(v2max)); text(v3x,v3min-0.003,num2str(v3min)); text(v4x,v4max+0.003,num2str(v4max)); text(v5x-1,v5min-0.003,num2str(v5min)); fprintf('4.挠曲线图如图所示\n\n'); %用能量法求各段最大挠度 M_1=x; M_21=-(l1+l2-v2x)/l2*(x-l1);M_22=(v2x-l1)/l2*(x-l1-l2); M_31=-(l1+l2+l3-v3x)/l3*(x-l1-l2);M_32=(v3x-l1-l2)/l3*(x-l1-l2-l3); M_41=-(l1+l2+l3+l4-v4x)/l4*(x-l1-l2-l3);M_42=(v4x-l1-l2-l3)/l4*(x-l1-l2-l3-l4); M_5=-x+l1+l2+l3+l4+l5; f11=int(2*M1*M_1/(E*Wz1*h1),x,0,l1);f10=-theta1C*l1;f1=f11+f10; f21=int(2*M2*M_21/(E*Wz2*h2),x,l1,v2x);f22=int(2*M2*M_22/(E*Wz2*h2),x,v2x,l1+l2);f2=f21+f22; f31=int(2*M3*M_31/(E*Wz2*h2),x,l1+l2,v3x);f32=int(2*M3*M_32/(E*Wz2*h2),x,v3x,l1+l2+l3);f3=f31+f32; f41=int(2*M4*M_41/(E*Wz2*h2),x,l1+l2+l3,v4x);f42=int(2*M4*M_42/(E*Wz2*h2),x,v4x,l1+l2+l3+l4);f4=f41+f42; f51=int(2*M5*M_5/(E*Wz3*h3),x,l1+l2+l3+l4,l1+l2+l3+l4+l5);f50=theta4G*l5;f5=f50+f51; f1=double(subs(f1));f2=double(subs(f2));f3=double(subs(f3));f4=double(subs(f4));f5=double(subs(f5)); A=[abs(f1),abs(f2),abs(f3),abs(f4),abs(f5)]; fmax=max(A); num=find(fmax==A); fmax=eval(['f',num2str(num)]); fmax_x=eval(['v',num2str(num),'x']); fprintf('各段的最大挠度为：\nf1max= %.5fm\nf2max= %.6fm\nf3max= %.5fm\nf4max= %.5fm\nf5max= %.4fm\n\n',f1,f2,f3,f4,f5); fprintf('综